Answer:
The degrees of freedom are given by:
[tex] df = n-1=14-1=13[/tex]
The significance level is [tex]\alpha=0.05[/tex] and then the critical value can be founded in th chi square table we need a quantile that accumulates 0.05 of the area in the right tail of the distribution and for this case is:
[tex] \chi^2_{\alpha}= 22.362[/tex]
And if the chi square statistic is higher than the critical value we can reject the null hypothesis in favor of the alternative.
Step-by-step explanation:
We have the followign system of hypothesis:
Null hypothesis: [tex]\sigma^2 \leq 3.5[/tex]
Alternative hypothesis: [tex] \sigma^2 >3.5[/tex]
The degrees of freedom are given by:
[tex] df = n-1=14-1=13[/tex]
The significance level is [tex]\alpha=0.05[/tex] and then the critical value can be founded in th chi square table we need a quantile that accumulates 0.05 of the area in the right tail of the distribution and for this case is:
[tex] \chi^2_{\alpha}= 22.362[/tex]
And if the chi square statistic is higher than the critical value we can reject the null hypothesis in favor of the alternative.
